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Imperfect preventive maintenance policies for two-process cumulative damage model of degradation and random shocks

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Abstract

In numerous applications, the system may fail due to multiple competing risks, especially degradation processes and random shocks. In this paper, we develop a two-process combination model for degraded system subject to cumulative effect from random shocks and degradation with two kinds of path function, including additive and multiplicative. Two numerical examples with sensitivity analysis for additive and multiplicative degradation path are discussed separately to illustrate this combination model. Based on the definition of the cumulative damage system, the imperfect preventive maintenance policy (N*, T*) with a common improvement factor is obtained to minimize the expected maintenance cost rate. The uncertainty of the reliability estimation and maintenance optimization is considered in the problem modeling. Also some extensions for this combination model are suggested for further research.

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References

  • Abdelaziz AR (1999) A fuzzy-based power system reliability evaluation. Electr Power Syst Res 50(1):1–5

    Article  Google Scholar 

  • Bae SJ, Kvam PH (2005) A nonlinear random coefficients model for degradation testing. Technometrics 46(4):460–469

    Article  MathSciNet  Google Scholar 

  • Bai J-M, Ze-Hui L, Kong X-B (2006) Generalized shock models based on a cluster point process. IEEE Trans Reliab 55(3):542–550

    Article  Google Scholar 

  • Chen J, Li Z (2008) An extended extreme shock maintenance model for a deteriorating system. Reliab Eng Syst Saf 93:1123–1129

    Article  Google Scholar 

  • Chiodo E, Mazzanti G (2006) Indirect reliability estimation for electric devices via a dynamic ‘stress-strength’ model. In: SPEEDAM 2006 international symposium on power electronics, electrical drives, automation and motion, Taormina

  • Ciampoli M (1998) Time dependent reliability of structural systems subject to deterioration. Comput Struct 67:29–35

    Article  MATH  Google Scholar 

  • Deloux E, Castanier B, Berenguer C (2009) Predictive maintenance policy for a gradually deteriorating system subject to stress. Reliab Eng Syst Saf 94(2):418–431

    Article  Google Scholar 

  • Ding Y, Lisnianski A (2008) Fuzzy universal generating functions for multi-state system reliability assessment. Fuzzy Sets Syst 159(3):307–324

    Article  MathSciNet  MATH  Google Scholar 

  • Fukada M (1991) Reliability and degradation of semiconductor lasers and LEDs. Artech House, Boston

    Google Scholar 

  • Gut A (2001) Mixed shock models. Bernoulli 7(3):541–555

    Article  MathSciNet  MATH  Google Scholar 

  • Hosseini MM, Kerr RM, Randall RB (2000) An inspection model with minimal and major maintenance for a system with deterioration and Poisson failures. IEEE Trans Reliab 49(1):88–987

    Article  Google Scholar 

  • Klutke G-A, Yang Y (2002) The availability of inspected systems subject to shocks and graceful degradation. IEEE Trans Reliab 51(3):371–374

    Article  Google Scholar 

  • Lehmann A (2009) Joint modeling of degradation and failure time data. J Stat Plan Inference 139(5):1693–1706

    Article  MathSciNet  MATH  Google Scholar 

  • Li Z (1984) Some probability distribution on Poisson shocks and its application in city traffic. J Lanzhou Univ 20:127–136

    Google Scholar 

  • Li WJ, Pham H (2005a) Reliability modeling of multi-state degraded systems with multi-competing failures and random shocks. IEEE Trans Reliab 54(2):297–303

    Article  Google Scholar 

  • Li WJ, Pham H (2005b) An inspection-maintenance model for systems with multiple competing processes. IEEE Trans Reliab 54(2):318–327

    Article  Google Scholar 

  • Lu CJ, Meeker WQ (1993) Using degradation measures to estimate of time-to-failure distribution. Technometrics 35:161–176

    Article  MathSciNet  MATH  Google Scholar 

  • Mallor F, Santos J (2003a) “Classification of shock model in system reliability”, Monografias del Semin. Matem Garcia de Galdeano 27:405–412

    MathSciNet  Google Scholar 

  • Mallor F, Santos J (2003b) Reliability of systems subject to shocks with a stochastic dependence for the damages. Test 12(2):427–444

    Article  MathSciNet  MATH  Google Scholar 

  • Mallor F, Omey E, Santos J (2006) Asymptotic results for a run and cumulative mixed shock model. J Math Sci 138(1):5410–5414

    Article  MathSciNet  MATH  Google Scholar 

  • Mori Y, Ellingwood BR (1994) Maintaining: reliability of concrete structures I: role of inspection/repair. Struct Eng 120(3):824–845

    Article  Google Scholar 

  • Nakagawa T (2007) Shock and damage models in reliability theory. Springer, NY

    MATH  Google Scholar 

  • Peng H, Feng Q, Coit DW (2009) Reliability modeling for MEMS devices subjected to multiple dependent competing failure processes. In: Proceedings of the 2009 industrial engineering research conference, Miami

  • Peng H, Feng Q, Coit DW (2009) Simultaneous quality and reliability optimization for microengines subject to degradation. IEEE Trans Reliab 58(1)

  • Persona A, Sgarbossa F, Pham H (2010) Age replacement policy in a random environment using systemability. Int J Syst Sci 41(11):1393–1397

    Article  Google Scholar 

  • Pham H (2005) A new mathematical reliability function considering operational environments. Int J Performab Eng 1(2)

  • Pham H, Wang H (1996) Imperfect maintenance. Eur J Oper Res 94:425–438

    MATH  Google Scholar 

  • Sanchez A, Carlos S, Martorell S, Jose F (2009) Villanueva, “Addressing imperfect maintenance modeling uncertainty in unavailability and cost based optimization”. Reliab Eng Syst Saf 94:22–32

    Article  Google Scholar 

  • Satow T, Teramoto K, Nakagawa T (2000) Optimal replacement policy for a cumulative damage model with time deterioration. Math Comput Model 31:313–319

    Article  MathSciNet  MATH  Google Scholar 

  • Sgarbossa F, Pham H (2010) A cost analysis of systems subject to random field environments and reliability. IEEE Trans Syst Man Cybernet C 40(4):429–437

    Article  Google Scholar 

  • Tanner DM, Smith NF, Irwin LW, Eaton WP, Helgesen KS, Clement JJ, Miller WM, Walraven JA, Peterson KA, Tangyunyong P, Dugger MT, Miller SL (2000) MEMS reliability: infrastructure, test structures, experiments, and failure modes. Sandia National Laboratories, Albuquerque, NM 87185-1081

  • van Noortwijk JM, Pandey MD (2003) A stochastic deterioration process for time-dependent reliability analysis. In: Proceedings of the eleventh IFIP WG 7.5 working conference on reliability and optimization of structural systems, pp 259–265

  • van Noortwijk JM, Van der Weide JAM, Kallen MJ, Pandey MD (2007) Gamma processes and peaks-over-threshold distribution for time-dependent reliability. Reliab Eng Syst Saf 92:1651–1658

    Article  Google Scholar 

  • Wang H, Pham H (2006) Reliability and optimal maintenance. Springer, NY

    MATH  Google Scholar 

  • Zehui L, Kong X (2007) Life behavior of δ-shock model. Stat Probab Lett 77(6):577–587

    Article  MATH  Google Scholar 

  • Zehui L, Zhao P (2007) Reliability analysis on the δ-shock model of complex systems. IEEE Trans Reliab 56(2):340–348

    Article  Google Scholar 

  • Zuo MJ, Jiang R, Yam RCM (1999) Approaches for reliability modeling of continuous-state devices. IEEE Trans Reliab 48(1):9–18

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Industrial and Systems Engineering, Rutgers University, New Brunswick, NJ, USA

    Yaping Wang & Hoang Pham

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  1. Yaping Wang
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  2. Hoang Pham
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Correspondence to Hoang Pham.

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Wang, Y., Pham, H. Imperfect preventive maintenance policies for two-process cumulative damage model of degradation and random shocks. Int J Syst Assur Eng Manag 2, 66–77 (2011). https://doi.org/10.1007/s13198-011-0055-8

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  • DOI: https://doi.org/10.1007/s13198-011-0055-8

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